Codazzi-Closed Anisotropic Metric Branches and Standard Model Multiplicity

A four-dimensional anisotropic metric branch is defined for traceless gauge-side stress tensors of non-null Rainich type. The construction is motivated by the Alena Tensor correspondence between flat force-density and curvilinear geometric descriptions, but the branch data are fixed locally. The branch has a 2+2 form with one anisotropy field. This field is obtained both from the gauge stress and from a normalized vorticity-flux closure, while the remaining tensor-force term is represented by the Levi-Civita geometry only when a trace-adjusted branch tensor satisfies the Codazzi condition. Under these restrictions, the closed branch gives a common geometric language for elementary-mode data. Mass is read as scalar curvature response, electric charge as transverse-frame holonomy, and color as a three-dimensional multiplicity space of equivalent self-dual branch modes. After a two-dimensional weak space is adjoined, preservation of the top form gives S(U(3) \times U(2)), and the even exterior algebra gives the anomaly-free representation content of one Standard Model generation, including \nu_L^c. The same branch normalization fixes a primitive coupling $g_B$; with G_F and one intermediate scale E_B=2.64\times10^{14}\,\mathrm{GeV} as inputs, the resulting branch-level one-loop evaluation gives a consistency check for m_W, m_Z, m_h, and \alpha_s(m_Z). The numerical Yukawa matrices, confinement energy, and global family spectrum are left as dynamical problems.